WJEC Further Unit 2 2019 June — Question 2

Exam BoardWJEC
ModuleFurther Unit 2 (Further Unit 2)
Year2019
SessionJune
TopicDiscrete Probability Distributions
TypeApply E(aX+b) or Var(aX+b) formulas directly

2. The probability of winning a certain game at a funfair is \(p\). Aman plays the game 5 times and Boaz plays the game 8 times. The independent random variables \(X\) and \(Y\) denote the number of wins for Aman and Boaz respectively.
  1. Given that \(\mathrm { E } ( X Y ) = 6 \cdot 4\), calculate \(p\).
  2. Find \(\operatorname { Var } ( X Y )\).